A finite element method to approximate the vibration modes of a structure in contact with an incompressible fluid is analyzed in this paper. The effect of the fluid is taken into account by means of an added mass formulation, which is one of the most usual procedures in engineering practice. Gravity waves on the free surface of the liquid are also considered in the model. Piecewise linear continuous elements are used to discretize the solid displacements, the variables to compute the added mass terms and the vertical displacement of the free surface, yielding a non conforming method for the spectral coupled problem. Error estimates are settled for approximate eigenfunctions and eigenfrequencies. Implementation issues are discussed and numerical experiments are reported. In particular the method is compared with other numerical scheme, based on a pure displacement formulation, which has been recently analyzed.
In this article, the optimal design of a road joining two terminals is investigated. A geometric model is proposed including horizontal transition curves and vertical curves, obtaining parameterizations for the central axis of the road as well as for its entire surface. These parameterizations allow to express and compute, with great simplicity, the major infrastructure costs, including land acquisition, clearance, pavement, maintenance, and earthwork, where multiple layers of materials with different costs can be handled. The road design problem is formulated as a smooth constrained optimization problem and a two-stage algorithm is suggested for its numerical resolution. Finally, numerical results are presented in an academic test and in a case study that propose designing a bypass in a Spanish national road (N-640) to avoid crossing Monterroso's town center.
SUMMARYA ÿnite element method to approximate the vibration modes of a plate in contact with an incompressible uid is analysed in this paper. The e ect of the uid is taken into account by means of an added mass formulation, discretized by standard piecewise linear tetrahedral ÿnite elements. Gravity waves on the free surface of the liquid are considered in the model. The plate is modelled by Reissner-Mindlin equations discretized by MITC3 locking-free elements.Implementation issues are discussed and numerical experiments are presented. In particular, the method is compared with analytical approximations and with an experimental study which has been recently reported.
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